{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:HFUB2KXHCL3HCVAQWIXZOQCC22","short_pith_number":"pith:HFUB2KXH","schema_version":"1.0","canonical_sha256":"39681d2ae712f6715410b22f974042d6a84e4d3ba0f53b01852d86d0fcdc55ea","source":{"kind":"arxiv","id":"1111.6578","version":2},"attestation_state":"computed","paper":{"title":"On the density of polyharmonic splines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jeremy Levesley, Thomas Hangelbroek","submitted_at":"2011-11-28T20:55:02Z","abstract_excerpt":"This article treats the question of fundamentality of the translates of a polyharmonic spline kernel (also known as a surface spline) in the space of continuous functions on a compact set $\\Omega\\subset \\RR^d$ when the translates are restricted to $\\Omega$. Fundamentality is not hard to demonstrate when a low degree polynomial may be added or when translates are permitted to lie outside of $\\Omega$; the challenge of this problem stems from the presence of the boundary, for which all successful approximation schemes require an added polynomial.\n  When $\\Omega$ is the unit ball, we demonstrate t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1111.6578","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-11-28T20:55:02Z","cross_cats_sorted":[],"title_canon_sha256":"366166438954ec737dcbe71003864f287240d39f898e3025772a5fb83b4eb6c7","abstract_canon_sha256":"0d6503b4fc03ae35323147c74f0e858c24c2669bdff4f43dbf52717ac089058b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:41.611612Z","signature_b64":"afZcDx+RzNm1uCNDdqgB7oBwEgol7fLrInjweuayeyzt2mwJTJvcC1CzHXbNTjkO9734bXPwsd1nwqpMs7WSBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39681d2ae712f6715410b22f974042d6a84e4d3ba0f53b01852d86d0fcdc55ea","last_reissued_at":"2026-05-18T03:37:41.611137Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:41.611137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the density of polyharmonic splines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jeremy Levesley, Thomas Hangelbroek","submitted_at":"2011-11-28T20:55:02Z","abstract_excerpt":"This article treats the question of fundamentality of the translates of a polyharmonic spline kernel (also known as a surface spline) in the space of continuous functions on a compact set $\\Omega\\subset \\RR^d$ when the translates are restricted to $\\Omega$. Fundamentality is not hard to demonstrate when a low degree polynomial may be added or when translates are permitted to lie outside of $\\Omega$; the challenge of this problem stems from the presence of the boundary, for which all successful approximation schemes require an added polynomial.\n  When $\\Omega$ is the unit ball, we demonstrate t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6578","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1111.6578","created_at":"2026-05-18T03:37:41.611205+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.6578v2","created_at":"2026-05-18T03:37:41.611205+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6578","created_at":"2026-05-18T03:37:41.611205+00:00"},{"alias_kind":"pith_short_12","alias_value":"HFUB2KXHCL3H","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"HFUB2KXHCL3HCVAQ","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"HFUB2KXH","created_at":"2026-05-18T12:26:30.835961+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HFUB2KXHCL3HCVAQWIXZOQCC22","json":"https://pith.science/pith/HFUB2KXHCL3HCVAQWIXZOQCC22.json","graph_json":"https://pith.science/api/pith-number/HFUB2KXHCL3HCVAQWIXZOQCC22/graph.json","events_json":"https://pith.science/api/pith-number/HFUB2KXHCL3HCVAQWIXZOQCC22/events.json","paper":"https://pith.science/paper/HFUB2KXH"},"agent_actions":{"view_html":"https://pith.science/pith/HFUB2KXHCL3HCVAQWIXZOQCC22","download_json":"https://pith.science/pith/HFUB2KXHCL3HCVAQWIXZOQCC22.json","view_paper":"https://pith.science/paper/HFUB2KXH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.6578&json=true","fetch_graph":"https://pith.science/api/pith-number/HFUB2KXHCL3HCVAQWIXZOQCC22/graph.json","fetch_events":"https://pith.science/api/pith-number/HFUB2KXHCL3HCVAQWIXZOQCC22/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HFUB2KXHCL3HCVAQWIXZOQCC22/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HFUB2KXHCL3HCVAQWIXZOQCC22/action/storage_attestation","attest_author":"https://pith.science/pith/HFUB2KXHCL3HCVAQWIXZOQCC22/action/author_attestation","sign_citation":"https://pith.science/pith/HFUB2KXHCL3HCVAQWIXZOQCC22/action/citation_signature","submit_replication":"https://pith.science/pith/HFUB2KXHCL3HCVAQWIXZOQCC22/action/replication_record"}},"created_at":"2026-05-18T03:37:41.611205+00:00","updated_at":"2026-05-18T03:37:41.611205+00:00"}